Skip to main content
SpringerLink
Log in

Quasiclassical theory of the upper critical field of high-field superconductors. Application to momentum-dependent scattering

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

A theory of the upper critical field is developed which is sufficiently general to incorporate strong coupling effects, anisotropy of both Fermi surface and pairing interaction, and momentum dependent scattering, including exchange and spin-orbit scattering. It is not necessary to assume that spin-orbit scattering is a small fraction of the total scattering. An important improvement in this theory is the correct treatment of the spatial dependence of the anomalous Green function and the order parameter in the mixed state. In the presence of anisotropy this is, in general, not described with sufficient accuracy by the Abrikosov vortex lattice. Application of this theory to anisotropy effects, with the clean limit taken in most cases, have been published elsewhere and additional studies will appear in the near future. In this paper we concentrate on the effects arising from the momentum dependence of the elastic scattering. If spin-orbit scattering forms a sizeable fraction of the total scattering it is necessary to take its explicit momentum dependence into account. When this is done we find that spin-orbit scattering is actually less effective in reducing paramagnetic limiting.p- andd-wave scattering have a marked effect on the upper critical fieldH c2 at low reduced temperatures, partially cancelling each other.d-wave scattering raisesH c2(O), but for physically acceptable parameter value is not sufficient to explain the apparent absence of paramagnetic limiting in some high-field superconductors. For a complete description of the upper critical field, other effects mentioned above need to be taken into account, but for superconductors of intermediate purity the momentum dependence of the scattering cannot be ignored. The greatest problem remaining in our quest for a complete understanding of the upper critical field appears to be an accurate determination of the relevant normal state properties.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. M. Clogston,Phys. Rev. Lett. 9, 266 (1962).

    Google Scholar 

  2. B. S. Chandrasekhar,Appl. Phys. Lett. 1, 7 (1962).

    Google Scholar 

  3. N. R. Werthamer, E. Helfand, and P. C. Hohenberg,Phys. Rev. 147, 295 (1966); N. R. Werthamer; inSuperconductivity, R. D. Parks, ed. (Marcel Dekker, New York, 1969), p. 321.

    Google Scholar 

  4. T. P. Orlando, E. J. McNiff, Jr., S. Foner, and M. R. Beasley,Phys. Rev. B 19, 4545 (1979).

    Google Scholar 

  5. R. Flükiger, S. Foner, and E. J. McNiff, Jr., inSuperconductivity in d- and f-Band Metals, H. Suhl and M. B. Maple, eds. (Academic Press, New York, 1980), p. 265.

    Google Scholar 

  6. S. A. Alterovitz and J. A. Woollam,Solid State Commun. 25, 141 (1978);Phil. Mag. B 40, 497 (1979);J. Magn. Magnetic Mat. 11, 177 (1979).

    Google Scholar 

  7. M. Decroux, Ø. Fischer, C. Rossel, B. Lachal, R. Baillif, R. Chevrel, and M. Sergent, inTernary Superconductors, G. K. Shenoy, B. P. Dunlap, and F. Y. Fradin, eds. (Elsevier, New York, 1981) p. 65.

    Google Scholar 

  8. G. H. Bongi, R. Flükiger, A. Trevaud, and Ø. Fischer,J. Low Temp. Phys. 23, 543 (1976).

    Google Scholar 

  9. M. R. Beasley, inAdvances in Cryogenic Engineering Matierals, R. P. Reed and A. F. Clark, eds. (Plenum, New York, 1982) vol. 28, p. 345.

    Google Scholar 

  10. T. P. Orlando and M. R. Beasley,Phys. Rev. Lett. 46, 1598 (1981).

    Google Scholar 

  11. G. Eilenberger,Z. Physik 214, 195 (1968).

    Google Scholar 

  12. A. I. Larkin and Yu. N. Ovchinnikov,Zh. Eksp. Teor. Fiz. 55, 2262 (1968); (Sov. Phys.-JETP 28, 1200 (1969)); J. W. Serene and D. Rainer,Phys. Reports 101, 221 (1983).

    Google Scholar 

  13. G. Eilenberger,Phys. Rev. 153, 584 (1967).

    Google Scholar 

  14. P. Fulde and K. Maki,Phys. Rev. 141, 275 (1966).

    Google Scholar 

  15. Ø. Fischer,Helv. Phys. Acta 45, 331 (1972).

    Google Scholar 

  16. W. Pint and E. Schachinger,Physica C 159, 33 (1989).

    Google Scholar 

  17. B. Hillenbrand, K. Schuster, and M. Wilhelm,Phys. Lett. 36A, 383 (1971); Ø. Fischer, M. Decroux, S. Roth, R. Chevrel, and M. Sergent,J. Phys. C: Solid State Phys. 8, L474 (1975); H. W. Meul, C. Rossel, M. Decroux, Ø. Fischer, G. Remenyi, and A. Briggs,Phys. Rev. Lett. 53, 497 (1984); Ø. Fischer, H. W. Meul, M. G. Karkut, G. Remenyi, U. Welp, J. C. Piccoche and K. Maki,Phys. Rev. Lett. 55, 2972 (1985); J. Cors, R. Baillif, M. G. Karkut, M. Decroux, Ø. Fischer, U. Welp, and G. Bruls,Europhys. Lett. 3, 635 (1987); G. K. Shenoy and S. K. Malik,Phys. Rev. B 33, 6132 (1986).

    Google Scholar 

  18. M.-T. Béal-Monod and R. A. Weiner,Phys. Rev. 170, 552 (1968).

    Google Scholar 

  19. M. B. Maple,Appl. Phys. 9, 179 (1976).

    Google Scholar 

  20. N. Schopohl and K. Scharnberg,Physica B 107, 293 (1981); LT-17 (Contributed Papers), U. Eckern, A. Schmid, and W. Weber, eds. (North-Holland, Amsterdam, 1984) p. 1039;Physica B 135, 482 (1985).

    Google Scholar 

  21. C. T. Rieck, Diplomarbeit, University of Hamburg (1987), unpublished.

  22. P. Vashishta and K. S. Singwi,Phys. Rev. B 6, 875 (1972).

    Google Scholar 

  23. L. W. Gruenberg and L. Gunther,Phys. Rev. 176, 606 (1968).

    Google Scholar 

  24. Z. Tešanović, M. Rasolt, and L. Xing,Phys. Rev. Lett. 63, 2425 (1989);Phys. Rev. B 43 288 (1991); C. T. Rieck, K. Scharnberg, and R. A. Klemm,Physica C 170, 195 (1990).

    Google Scholar 

  25. A. M. Clogston and V. Jaccarino,Phys. Rev. 121, 1357 (1961).

    Google Scholar 

  26. L. F. Mattheiss and W. Weber,Phys. Rev. B 25, 2248 (1982).

    Google Scholar 

  27. P. Horsch and H. Rietschel,Z. Physik B 27, 153 (1977); M. D. Whitmore and J. P. Carbotte,J. Low Temp. Phys. 47, 411 (1982); W. E. Pickett,Phys. Rev. B 21, 3897 (1980).

    Google Scholar 

  28. B. Cort, G. R. Stewart, S. Z. Huang, R. L. Meng, and C. W. Chu,Phys. Rev. B 24, 5058 (1981).

    Google Scholar 

  29. G. R. Stewart, inSuperconductivity in d- and f-Band Metals 1982, W. Buckel and W. Klose, eds. (Kernforschungszentrum, Karlsruhe, 1982), p. 81.

    Google Scholar 

  30. G. Kieselmann and H. Rietschel,J. Low Temp. Phys. 46, 27 (1982); E. Schachinger and J. P. Carbotte,J. Phys. F: Metal Phys. 13, 2615 (1983).

    Google Scholar 

  31. M. Schossmann and E. Schachinger,Phys. Rev. B 30, 1349 (1984).

    Google Scholar 

  32. T. P. Orlando, J. A. Alexander, S. J. Bending, J. Kwo, S. J. Poon, R. H. Hammond, M. R. Beasley, E. J. McNiff, Jr., and S. Foner,IEEE Trans. Magn. MAG-17, 368 (1981).

    Google Scholar 

  33. J. P. Carbotte,Rev. Mod. Phys. 62, 1027 (1990).

    Google Scholar 

  34. D. Rainer, G. Bergmann and U. Eckhardt,Phys. Rev. B 8, 5324 (1973).

    Google Scholar 

  35. D. Rainer and G. Bergmann,J. Low Temp. Phys. 14, 501 (1974).

    Google Scholar 

  36. M. Schossmann and E. Schachinger,Phys. Rev. B 33, 6123 (1986).

    Google Scholar 

  37. J. W. Wilkins, inElectrons at the Fermi Surface, M. Springford, ed. (Cambridge University Press, London, 1980), p. 91.

    Google Scholar 

  38. D. Rainer,3rd Winter Meeting on Low Temperature Physics, Hacienda Cocoyoc (1982), unpublished.

  39. J. F. Janak,Phys. Rev. B 16, 255 (1977); H. Rietschel and H. Winter,Phys. Rev. Lett. 43, 1256 (1979); H. Rietschel, H. Winter, and W. Reichardt,Phys. Rev. B 22, 4284 (1980).

    Google Scholar 

  40. P. M. Gedrow, J. T. Kucera, D. Rainer, and T. P. Orlando,Phys. Rev. Lett. 52, 1637 (1984); J. A. Alexander, T. P. Orlando, D. Rainer and P. M. Tedrow,Phys. Rev. B 31, 5811 (1985).

    Google Scholar 

  41. E. Schachinger, H. G. Zarate, M. Schossmann, and J. P. Carbotte,J. Low Temp. Phys. 63, 1 (1986).

    Google Scholar 

  42. O. K. Andersen, W. Klose and H. Nohl,Phys. Rev. B 17, 1209 (1978).

    Google Scholar 

  43. Y. Yafet, inSolid State Physics, F. Seitz and D. Turnbull, eds. (Academic, New York, 1963) vol. 14, p. 75.

    Google Scholar 

  44. F. P. Marin and H. Suhl,Phys. Rev. Lett. 63, 442 (1989).

    Google Scholar 

  45. D. Markowitz and L. P. Kadanoff,Phys. Rev. 131, 563 (1963).

    Google Scholar 

  46. M. Prohammer and E. Schachinger,Phys. Rev. B 36, 8353 (1987).

    Google Scholar 

  47. K. Scharnberg and R. A. Klemm,Phys. Rev. Lett. 54, 2445 (1985); R. A. Klemm and K. Scharnberg,Physica B 135, 53 (1985); R. A. Klemm and K. Scharnberg,J. Magn. Magnetic Mat. 54–57, 381 (1986).

    Google Scholar 

  48. M. Prohammer and J. P. Carbotte,Phys. Rev. B 42, (1990) 2032.

    Google Scholar 

  49. K. Machida, T. Ohmi, and M. Ozaki,J. Phys. Soc. Jpn. 54, 1552 (1985); M. E. Zhitomirskii,Zh. Eksp. Teor. Fiz. 97, 1346 (1990); (Sov. Phys. JETP 70, 760 (1990)).

    Google Scholar 

  50. L. I. Burlachkov,Physica C 166, 25 (1990).

    Google Scholar 

  51. W. H. Butler,Phys. Rev. Lett. 44, 1516 (1980).

    Google Scholar 

  52. K. Scharnberg and R. A. Klemm,Phys. Rev. B 22, 5233 (1980).

    Google Scholar 

  53. C. T. Rieck and K. Scharnberg,Physica B 163, 670 (1990).

    Google Scholar 

  54. C. T. Rieck, Dissertation, University of Hamburg (1991), unpublished.

  55. C. T. Rieck, Th. Wölkhausen, D. Fay, and L. Tewordt,Phys. Rev. B 39, 278 (1989).

    Google Scholar 

  56. H. J. Zeiger and G. W. Pratt,Magnetic Interactions in Solids (Clarendon, Oxford, 1973).

    Google Scholar 

  57. P. Fulde,Adv. Phys. 22, 667 (1973).

    Google Scholar 

  58. P. B. Allen, inModern Trends in the Theory of Condensed Matter, A. Pekalski and J. Przystawa, eds. (Springer, Berlin, 1980), p. 404.

    Google Scholar 

  59. D. J. Scalapino, inSuperconductivity, R. D. Parks, ed. (Marcel Dekker, New York, 1969), p. 449.

    Google Scholar 

  60. C. Gladstone, M. A. Jensen, and J. R. Schrieffer, inSuperconductivity, R. D. Parks, ed. (Marcel Dekker, New York, 1969), p. 665.

    Google Scholar 

  61. L. D. Landau and E. M. Lifschitz,Lehrbuch der Theoretischen Physik (Akademie-Verlag, Berlin, 1984) vol. IX, p. 229.

    Google Scholar 

  62. G. Bergmann,Phys. Rep. 27, 156 (1976); H. Takayama,J. Physique 5, C4-299 (1974); G. Grünewald and K. Scharnberg,Solid State Commun. 32, 955 (1979).

    Google Scholar 

  63. N. Schopohl,J. Low Temp. Phys. 41, 409 (1980).

    Google Scholar 

  64. A. J. Leggett,Rev. Mod. Phys. 47, 332 (1975).

    Google Scholar 

  65. F. J. Ohkawa and H. Fukuyama,J. Phys. Soc. Japan 53, 4344 (1984); F. J. Ohkawa, inTheory of Heavy Fermions and Valence Fluctuations, K. Kasuya and T. Saso, eds., Springer Series in Solid State Sciences, vol. 62, p. 242 (Springer, Berlin, 1985).

    Google Scholar 

  66. P. Fulde, J. Keller, and G. Zwicknagel, inSolid State Physics, H. Ehrenreich and D. Turnbull eds. (Academic, New York, 1988), vol. 41, p. 1.

    Google Scholar 

  67. J. R. Schrieffer, X. G. Wen, and S. C. Zhang,Phys. Rev. B 39, 11663 (1989).

    Google Scholar 

  68. R. Balian and N. R. Werthamer,Phys. Rev. 131, 1553 (1963).

    Google Scholar 

  69. V. L. Berezinskii,Pis'ma Zh. Eksp. Teor. Fiz. 20, 628 (1974); (JETP Lett. 20, 287 (1974)).

    Google Scholar 

  70. D. R. Tilley, G. J. van Gurp and C. W. Berghout,Phys. Lett. 12, 305 (1964).

    Google Scholar 

  71. L. Dobrosavljevic and H. Raffy,Phys. Stat. Sol. 64, 229 (1974); D. R. Tilley,Proc. Phys. Soc. 85, 1177 (1965).

    Google Scholar 

  72. R. A. Klemm, A. Luther and M. R. Beasley,Phys. Rev. B 12, 877 (1975).

    Google Scholar 

  73. W. H. Kleiner, L. M. Roth, and S. H. Autler,Phys. Rev. 133, A1226 (1964).

  74. R. P. Hübener,Magnetic Flux Structures in Superconductors (Springer Verlag, Berlin, 1979).

    Google Scholar 

  75. P. C. Hohenberg and N. R. Werthamer,Phys. Rev. 153, 493 (1966).

    Google Scholar 

  76. E. Helfand and N. R. Werthamer,Phys. Rev. 147, 288 (1966).

    Google Scholar 

  77. H. Rietschel and H. Winter,Phys. Rev. Lett. 43, 1256 (1979); H. Rietschel, H. Winter, and W. Reichardt,Phys. Rev. B 22, 4284) (198)0.

    Google Scholar 

  78. G. Grimvall, inThe Electron-Phonon Interaction in Metals (North-Holland, Amsterdam, 1981).

    Google Scholar 

  79. K. Maki,Physics 1, 21 (1964);Phys. Rev. 148, 362 (1966).

    Google Scholar 

  80. Ø. Fischer,Appl. Phys. 16, 1 (1978).

    Google Scholar 

  81. M. Decroux, Ø. Fischer, R. Flükiger, B. Seeber, R. Delesclefs, and M. Sergent,Solid State Commun. 25, 393 (1978).

    Google Scholar 

  82. B. G. Pazol, D. J. Holmgren, and D. M. Ginsberg,J. Low Temp. Phys. 73, 229 (1988);J. Low Temp. Phys. 74, 133 (1989).

    Google Scholar 

  83. S. Foner and E. J. McNiff,Phys. Lett. 58A, 318 (1976).

    Google Scholar 

  84. G. E. Zwicknagl and J. W. Wilkins,Phys. Rev. Lett. 53, 1276 (1984).

    Google Scholar 

  85. R. J. Elliott,Phys. Rev. 96, 266 (1954).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Abteilung für Theoretische Festkörperphysik, Fachbereich Physik der Universität Hamburg, Hamburg, Germany

    C. T. Rieck & K. Scharnberg

  2. Institut Max von Laue-Paul Langevin, Grenoble, France

    N. Schopohl

Authors
  1. C. T. Rieck
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Scharnberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. Schopohl
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to L. Tewordt on the occasion of his 65th birthday.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rieck, C.T., Scharnberg, K. & Schopohl, N. Quasiclassical theory of the upper critical field of high-field superconductors. Application to momentum-dependent scattering. J Low Temp Phys 84, 381–464 (1991). https://doi.org/10.1007/BF00683526

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00683526

Keywords

Search

Navigation